Algebra 1 2023 Midterm

Front

What does it mean for a quantity to vary directly with another?

Back

A quantity varies directly with another if it increases or decreases in proportion to that quantity. For example, if the amount of gas consumed by a car varies directly with the miles driven, then doubling the miles driven will double the gas consumed.

Front

If a car uses 6 gallons of gas for 180 miles, how do you find the gas used for 1,260 miles?

Back

To find the gas used for 1,260 miles, set up a proportion: (6 gallons / 180 miles) = (x gallons / 1260 miles). Solving this gives x = 42 gallons.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How do you determine the domain and range from a graph?

Back

To determine the domain, look at the x-values covered by the graph. To determine the range, look at the y-values covered by the graph.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the ratio of the change in y to the change in x, often represented as 'slope'.

Front

How do you calculate the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a system of equations to have a solution?

Back

A system of equations has a solution if there is at least one set of values for the variables that satisfies all equations in the system.

Front

How do you solve a system of equations using substitution?

Back

To solve using substitution, solve one equation for one variable, then substitute that expression into the other equation.